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Read the following statements which are taken as axioms
(i) If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal.
(ii) If a transversal intersect two parallel lines, then alternate interior angles are equal.
Is this system of axioms consistent ? Justify your answer.
A system of axiom is called consistent, if there is no statement which can be deduced from these axioms such that it contradicts any axiom. We
know that, if a transversal intersects two parallel lines, then each pair of corresponding angles are equal, which is a theorem. So, Statement I is
false and not an axiom.
Also, we know that, if a transversal intersects two parallel lines, then each pair of alternate interior angles are equal. It is also a theorem. So,
Statement II is true and an axiom. . Thus, in given statements, first is false and second is an axiom.
Hence, given system of axioms is not consistent.